Multiplying a Unit Fraction by a Whole Number
4A · Chapter 8 · Lesson 1 · MATH-4A-C08-L01
Learning goal. Find one of b equal shares of a whole-number quantity and describe divisibility.
Before you begin
Recall: 4A Ch6/7: equal partitions, mixed numbers and fraction operations. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 1 5/6 − 1 2/3.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 5 1/2 − 1 1/2.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 2 3/4 − 1 1/2.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Key vocabulary
- unit fraction
- fraction with numerator one
- fraction of a set
- part of a discrete collection
- reference whole
- quantity to which a fraction applies
- remaining amount
- quantity after some part is removed
Understand the concept
Finding one unit fraction of a whole-number set means splitting the set into the denominator's equal groups. One fourth of 28 is one of four groups of seven objects, so it is seven. A diagram of equal groups makes the division step visible; an uneven grouping would not represent fourths of the whole.
Model it: equal-group counter array. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
What is 1/10 of 80 counters?
Partition 80 into 10 equal groups: 80 ÷ 10 = 8.
Check your understanding 1
What is 1/2 of 16 counters?
Show answer & reasoning
Partition 16 into 2 equal groups: 16 ÷ 2 = 8.
Worked example 2
What is 1/5 of 40 counters?
Partition 40 into 5 equal groups: 40 ÷ 5 = 8.
Check your understanding 2
What is 1/10 of 20 counters?
Show answer & reasoning
Partition 20 into 10 equal groups: 20 ÷ 10 = 2.
Worked example 3
What is 1/10 of 50 counters?
Partition 50 into 10 equal groups: 50 ÷ 10 = 5.
Check your understanding 3
What is 1/2 of 12 counters?
Show answer & reasoning
Partition 12 into 2 equal groups: 12 ÷ 2 = 6.
Guided practice
What is 1/3 of 15 counters?
Show answer & reasoning
Partition 15 into 3 equal groups: 15 ÷ 3 = 5.
What is 1/2 of 6 counters?
Show answer & reasoning
Partition 6 into 2 equal groups: 6 ÷ 2 = 3.
What is 1/6 of 24 counters?
Show answer & reasoning
Partition 24 into 6 equal groups: 24 ÷ 6 = 4.
What is 1/8 of 72 counters?
Show answer & reasoning
Partition 72 into 8 equal groups: 72 ÷ 8 = 9.
What is 1/2 of 8 counters?
Show answer & reasoning
Partition 8 into 2 equal groups: 8 ÷ 2 = 4.
Independent practice
What is 1/8 of 48 counters?
Show answer & reasoning
Partition 48 into 8 equal groups: 48 ÷ 8 = 6.
What is 1/2 of 18 counters?
Show answer & reasoning
Partition 18 into 2 equal groups: 18 ÷ 2 = 9.
What is 1/2 of 4 counters?
Show answer & reasoning
Partition 4 into 2 equal groups: 4 ÷ 2 = 2.
What is 1/8 of 24 counters?
Show answer & reasoning
Partition 24 into 8 equal groups: 24 ÷ 8 = 3.
What is 1/2 of 10 counters?
Show answer & reasoning
Partition 10 into 2 equal groups: 10 ÷ 2 = 5.
What is 1/5 of 30 counters?
Show answer & reasoning
Partition 30 into 5 equal groups: 30 ÷ 5 = 6.
What is 1/6 of 12 counters?
Show answer & reasoning
Partition 12 into 6 equal groups: 12 ÷ 6 = 2.
What is 1/4 of 36 counters?
Show answer & reasoning
Partition 36 into 4 equal groups: 36 ÷ 4 = 9.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student finds one-fourth of 28 by multiplying 28 × 4. Explain and give the correct amount.
Show answer & reasoning
One fourth means dividing 28 into four equal groups; 28 ÷ 4 = 7.
What is 1/10 of 70 counters?
Show answer & reasoning
Partition 70 into 10 equal groups: 70 ÷ 10 = 7.
Exit check
What is 1/3 of 18 counters?
Show answer & reasoning
Partition 18 into 3 equal groups: 18 ÷ 3 = 6.
What is 1/4 of 16 counters?
Show answer & reasoning
Partition 16 into 4 equal groups: 16 ÷ 4 = 4.
What is 1/5 of 25 counters?
Show answer & reasoning
Partition 25 into 5 equal groups: 25 ÷ 5 = 5.